This dissertation studies the role of bounded rationality in New Keynesian models. In particular, I focus on ``cognitive discounting", the idea that agents discount variables far into the future at higher rates than typically implied in the benchmark model.

Chapter 1 estimates a Behavioral New Keynesian model to revisit the evidence that passive US monetary policy in the pre-1979 sample led to indeterminate equilibria and sunspot-driven fluctuations, while active policy after 1982 was instrumental in restoring macroeconomic stability. The model assumes cognitive discounting and we estimate the model allowing for both determinacy and indeterminacy. The empirical results show that determinacy is preferred both before and after 1979. Even if monetary policy is found to react only mildly to inflation in the pre-Volcker era, the estimated substantial degrees of bounded rationality prevent the economy from falling into indeterminacy.

In Chapter 2, I show how to introduce cognitive discounting into alternative models of larger sizes and with different expectational assumptions. I use this finding to build and estimate a Behavioral Smets and Wouters model, which is a medium-scale DSGE model. The empirical estimation shows that the data still prefer substantial degrees of bounded rationality even in a model with as many frictions as the Smets and Wouters model. Chapter 3 develops a New Keynesian model with trend inflation and cognitive discounting. In a model with rational expectations, higher trend inflation generates macroeconomic instability by making the economy more susceptible to equilibrium indeterminacy. The rational expectations hypothesis, however, implies a very large weight given to expectations far into the future, with only minimal discounting. Since determinacy or indeterminacy of the equilibrium is a property of the whole model, a failure to recognize and explicitly model deviations from benchmark models of expectations formation may skew the results. Indeed, the analysis shows that this instability hinges on the conventional assumption of rational expectations and that introducing cognitive discounting in the model counteracts the instability introduced by trend inflation and increases the scope for determinacy. Therefore, trend inflation is not as destabilizing as previously thought. Moreover, the data favor the specification including bounded rationality and a determinate equilibrium during the Great Moderation sample.